{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "134e7f9d",
   "metadata": {},
   "source": [
    "# Demo 2: Plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2571d531",
   "metadata": {},
   "source": [
    "Initialize KAN and create dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2075ef56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([1000, 2]), torch.Size([1000, 1]))"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from kan import *\n",
    "# create a KAN: 2D inputs, 1D output, and 5 hidden neurons. cubic spline (k=3), 5 grid intervals (grid=5).\n",
    "model = KAN(width=[2,5,1], grid=3, k=3, seed=1)\n",
    "\n",
    "# create dataset f(x,y) = exp(sin(pi*x)+y^2)\n",
    "f = lambda x: torch.exp(torch.sin(torch.pi*x[:,[0]]) + x[:,[1]]**2)\n",
    "dataset = create_dataset(f, n_var=2)\n",
    "dataset['train_input'].shape, dataset['train_label'].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c6add1d",
   "metadata": {},
   "source": [
    "Plot KAN at initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ac76f858",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot KAN at initialization\n",
    "model(dataset['train_input']);\n",
    "model.plot(beta=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8071b133",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# if you want to add variable names and title\n",
    "model.plot(beta=100, in_vars=[r'$\\alpha$', 'x'], out_vars=['y'], title = 'My KAN')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddf67e30",
   "metadata": {},
   "source": [
    "Train KAN with sparsity regularization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "97111d75",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 5.55e-02 | test loss: 5.69e-02 | reg: 5.02e+00 : 100%|██| 20/20 [00:12<00:00,  1.56it/s]\n"
     ]
    }
   ],
   "source": [
    "# train the model\n",
    "model.fit(dataset, opt=\"LBFGS\", steps=20, lamb=0.01, auto_save=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f30c3ab",
   "metadata": {},
   "source": [
    "$\\beta$ controls the transparency of activations. Larger $\\beta$ => more activation functions show up. We usually want to set a proper beta such that only important connections are visually significant. transparency is set to be ${\\rm tanh}(\\beta \\phi)$ where $\\phi$ is the scale of the activation function (metric='act') or the feature attribution score (metric='fa'). By default $\\beta=3$ and metric='fa'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3f95fcdd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gQXj11Vfx8ccf4/Lly9DpdFzR2BCWC1EDsFgaT5IktGjRAq+99hp27dqFzz77DJ07d0ZCQgIGDhyIl156CRs2bMAvv/yidFSSgST4pwLZMXM9/W2pjF599VX885//lO3+1Go1fvnlF2RnZ2PPnj24ePEievbsiU8//VS2f4PMj0eLEZFRWrVqhS+//FL2++3cuTMCAgJQUFAAtVot+/2TeXHlQnaNKxfj1dbWNvm/IUkSHBwcmvzfoabDciGiJnP7rxdbKli6P+7QJzIC/xYzzvHjx+Hg4IDjx48rHYXMjOVCRESyY7kQEZHsWC5ERCQ7lgsREcmO5UJERLJjuRARkexYLkREJDuWCxERyY7lQkREsmO5EBGR7FguREQkO5YLERHJjuVCRESyY7kQEZHsWC5ERCQ7lgsREcmO5UJERLJjuRARkexYLkREJDuWCxERyY7lQkREsmO5EBGR7FguREQkO5YLERHJjuVCRESyY7kQEZHsWC5ERCQ7lgsREcmO5UJERLJzVDpAYwghcOPGDVRUVMDd3R0+Pj6QJEnpWBaNMzNN3dzKy8vh4eHBuTWAEAIlJSUAgJKSEgghOLMGsJVt1CpXLqWlpUhKSkJgYCB8fX3h5+cHX19fBAYGIikpCaWlpUpHtDicmWn+PDd/f3/O7T5un9ngwYMhhMDgwYM5s/uwuW1UWJnMzEzh5uYmJEkSkiQJAIavuu+5ubmJzMxMpaNaDM7MNJyb8Tgz09ji3KyqXDIzM4WDg4NQqVT1hv/nL5VKJRwcHKzqB9FUODPTcG7G48xMY6tzk4QQQu7VUFMoLS1Fu3btoNFooNfr73t9lUoFV1dXFBQUwMvLq+kDWiDOzDScm/E4M9PY8tysZp/Lli1boFarG/QDAAC9Xg+1Wo2tW7c2cTLLxZmZhnMzHmdmGluem1WsXIQQCAwMRH5+PoyJK0kS/P39cf78eas82qIxODPTcG7G48xMY+tzs4pyuX79Onx9fRt1ex8fHxkTWT7OzDScm/E4M9PY+tys4mWxioqKRt2+vLxcpiTWgzMzDedmPM7MNLY+N6soF3d390bd3sPDQ6Yk1oMzMw3nZjzOzDS2PjerKBcfHx8EBAQY/fqiJEkICAhAy5YtmyiZ5eLMTMO5GY8zM42tz80qykWSJERERJh026lTp1r0Tq+mwpmZhnMzHmdmGlufm1Xs0Ads+3jwpsKZmYZzMx5nZhpbnptVrFwAwMvLC9u3b4ckSVCp7h1bpVJBkiR88cUXFv8DaEqcmWk4N+NxZqax6bmZ+5QAjdXQc/BkZWUpHdVicGam4dyMx5mZxhbnZnXlIoQQJSUlIikpSQQEBNT7IQQEBIikpCRRWlqqdESLw5mZhnMzHmdmGlubm1WWSx29Xi+ys7MFAJGdnS30er3SkSweZ2Yazs14nJlpbGVuVrPP5U4kSTK89ujl5WXxR09YAs7MNJyb8Tgz09jK3Ky6XIiIyDKxXIiISHYsFyIikh3LhYiIZMdyISIi2bFciIhIdiwXIiKSHcuFiIhkx3IhIiLZsVyIiEh2LBciIpIdy4WIiGTHciEiItmxXIiISHYsFyIikh3LhYiIZGe15VJRUYFz587h1KlTAIBr166hurpa4VSWr6KiApcuXQIA5OTk4PLly5zbfdTU1ODKlSvIyckBAOTl5eHmzZvQ6/UKJ7NsfK4Zz5Z+r0lCCKF0CGPk5+dj06ZN+Prrr3H58mXU1NSgqqoKLVq0QI8ePfD6669jxIgR8PDwUDqqRbl9bpcuXYJGo4GzszPc3NzQvXt3zu0OSktLsX37dnz44Yc4ffo0ysvLUV1djWbNmsHX1xfPPvss3nrrLQQFBcHR0VHpuBaDzzXj2eLvNaspF51Oh48++ggxMTHQaDQIDQ3FkCFD0KFDB+j1euTm5iIjIwN79+5Fz549sXbtWnTp0kXp2Irj3Exz6NAhREZG4uTJk+jduzeGDx+Oxx9/HO7u7igtLcXRo0exY8cO5Obm4pVXXsHixYvh6+urdGxF8blmPJuembACOp1OrFu3Tri5uYnQ0FBx4sQJUVtbKw4ePCiSkpJEUlKSyMnJEdXV1WLfvn3iySefFJ07dxanTp1SOrqiODfTZGVlidatW4vAwEDx+eefC7VaLUpLS0VaWppISkoS77//vtBoNOLWrVti48aNok2bNmLIkCHi2rVrSkdXDJ9rxrP1mVlFuezdu1d4eXmJl156Sdy8eVPo9XohhBCxsbECgAAgtm3bJoQQQq/Xi0uXLom+ffuKfv36iZKSEgWTK4tzM97Zs2eFn5+f6Natm/j3v/9tmFleXp7w9PQUAISfn5+4efOmEOL3ue3fv1+0a9dOjBkzRmi1WiXjK4bPNePZ+swsfoe+RqPBwoUL8eCDD2LNmjXw8vKCJEl3vb4kSWjfvj3Wrl2Lc+fO4YMPPjBjWsvBuRlPp9Nh6dKlKCkpQUpKCrp06XLPmQG/z61fv36Ij4/HV199hczMTDOltRx8rhnPHmZm8eVy9OhRHD58GOHh4Wjbtu19N3bg9x/E3/72N7z88svYvHkz1Gq1GZJaFs7NeLm5udixYwdGjBiBfv36NWhmwO9ze/HFF/H0008jPT0dtbW1TZzUsvC5Zjx7mJnFH+Ly/fffw8XFBYMHD0ZOTk69DbeoqMjw37/++itOnjxp+H8vLy+8+OKL+OCDD3Dx4kXr2QkmE87NeAcPHkRFRQVGjhyJixcvorKy0nBZQUEBdDodAKC6uhqnT59GixYtDJe3adMGI0aMwDvvvINr166hXbt2Zs+vFD7XjGcXM1P6dbn7GTNmjHjkkUfEuXPnRIcOHUSzZs0MX46OjobXJp2cnOpd9uabb4oLFy6IVq1aiYyMDKUfhtlxbsZ7++23hZeXl8jJyRHPP/98vbm4uLgYZiZJUr3LXF1dRWpqqjhw4IDw8PAQ//rXv5R+KGbF55rx7GFmFr1yEUJAq9XCxcUFDg4O0Gq10Gq1d7xuTU0NampqDP9fXV0NZ2dnw+3sCedmGo1GA0dHR7i4uKCqququj79uvrerra2Fq6srhBCoqqoyR1yLwOea8exlZhZdLpIkoVWrVjhy5Ah0Oh0GDhyI0tJSw+Xnz59Hfn4+AKB79+5o06aN4bLHH38cpaWlqKqqQsuWLc0dXVGcm2keeOABaDQalJaWok+fPnBzczNcptFocPDgQUOJ9O3b1/DGSUmS0KFDBxQXF0OlUsHb21uph2BWNTU1OHToEPLy8lBaWsrnWgPZzfap5LKpIdLT04Wrq6vYv3+/qK2trfcVExNjWD5u2bKl3mU6nU5s3rxZPPTQQ6KgoEDph2F2nJvxdu3aJZydnUVaWtpfZnbu3DnDocgPP/ywuH79+l/mFh0dLR555BGrOEzUVJcvXxabNm0SI0eOFF5eXkKlUgkPDw/RrFkzPteMYA/bp8UfLTZo0CB4eHhgy5YtEELAwcHB8KVS/f/4KpWq3mVarRZbt25Fv3798NBDDyn4CJTBuRnvqaeegr+/P7Zs2YLKysp6c3FwcDBcT5KkenNTqVS4evUqPv/8cwwfPhyenp4KPgp5VVdXY+/evYiOjsYTTzyBjh07IiwsDEVFRZgxYwb+9a9/4dixY2jRogWfa0awh+3T4svl4YcfxujRo/Hpp58iKysLogFnq9Hr9di8eTOOHz+OiIiIer8Y7AXnZjwfHx9MmTIFx44dQ3JycoMPKa6qqsKiRYug0WgwceLEBh/CbKkuXbqEDRs24L//+7/h6+uLwYMHY9u2bejZsyc++ugjFBUV4cCBA4iNjcWTTz4Jf39/k59rP/zwA3r06FHvF6o9sIvtU7lFU8NdvXpV9O7dW7Rv317s2bNH6HQ6IYQQ8+fPF46OjsLJyUl88MEHQq/Xi5qaGrFt2zbRqlUrERMTI2praxVOrxzOzXgVFRXi5ZdfFu7u7mL16tVCrVYLvV4v8vLyhI+Pj3B0dBSdOnUyvKO6rKxMvP3228LT01O89957Ssc3iVarFd9++62IiooSXbt2FSqVSjg5OYn+/fuLpUuXimPHjhmeO3dj6nPtmWeeEY899pgICwuzu9Pn2Pr2aRXlIoQQp0+fFj179hQtW7YUc+fOFbm5ueLcuXPi+++/F99//724dOmSOHnypAgLCxOenp5i8uTJorKyUunYiuPcjFdcXCz+/ve/C1dXV/Hiiy+Kffv2ieLiYnHgwAGxb98+cejQIfHbb7+JnTt3ioEDBwpvb2+xdu1aq9jg6+Tl5Yl169aJF154Qbi7uwuVSiXatWsnxo0bJz7//HOT9huZ+lzbu3ev6N+/v+jTp4/44osvDKdBsQe2vH1azVmRAeDKlStYtGgRPvnkEzg6OqJLly5o3749dDodLl68iLNnz8LHxwfR0dH4n//5H7i4uCgd2SJwbsarrKxEeno6kpOTUVRUBH9/fwQGBsLDwwMlJSU4e/YsCgsL0atXL8TFxaF///4W/dKORqPB/v37kZGRgczMTJw/fx6Ojo4ICgpCaGgogoOD0b1790a/pGfqc+3WrVtYsWIFvvzySwQFBWHhwoUWv09BLra6fVpVuQC/n/8pJycHO3fuxJEjR1BcXAwnJyf4+flh4MCBGDp0KB544AGlY1oczs00165dQ3Z2Nvbt24f8/HxotVp4e3ujW7duGDp0KPr06YPmzZsrHfMvhBDIzc1FZmYmMjIysG/fPmi1WrRv3x4hISEIDQ3FwIED651lQC6Nea4dOHAAcXFxqKiowNtvv42RI0da/T6shrDF7dPqyuV2QgjodDpIkmT5O7csCOdmGp1OByEEVCqVRa5SKisrsW/fPsPqJD8/H87OzujXrx9CQ0MREhKCxx57zKy/rE15rpWXl2PlypXYvn07+vbtiwULFtR7r4ets5Xt06rLhcieCSFw5swZZGZmIjMzEwcOHEBVVRUefvhhw+pkwIABcHd3VzqqSX788UfMnz8ft27dwsyZM/H3v//dIkud7ozlQmRFKioq8N133xkK5dKlS3BxcUH//v0REhKCkJAQPPLIIzbzUlJFRQVWrVqFzz77DE899RQWLVpkVycFtWYsFyILJoTA6dOnDWXyww8/oKamBp06dTKUSf/+/S1yv4+cDh06hPnz56OkpAQzZszAK6+8wlWMhWO5EFmYW7duITs7GxkZGcjKykJBQQFcXV0xYMAAQ6F06tRJ6ZhmV1lZiTVr1uCjjz5C7969sWjRIrRv317pWHQXLBcihQkhcPLkScPqpO4EmZ07dzbsO+nXrx9cXV2VjmoRjhw5gnnz5uH69euYPn06Ro8ezVWMBWK5ECmgtLQUe/bsMaxOrl69Cjc3NwwcONDwvhM/Pz+lY1ostVqNxMREfPjhh+jZsycWL16Mjh07Kh2LbsNyITIDvV6Pn3/+2bA6OXz4MHQ6Hbp06WJYnQQFBVnNG+QsxU8//YTY2FgUFxdj2rRpGDNmjFUfvmtLWC5ETeTGjRv49ttvkZmZid27d6OoqAju7u54/vnnDauTDh06KB3T6mm1WiQlJWHbtm144oknsHjxYq76LADLhUgmer0eP/30E7KyspCZmYkjR45Ar9fj8ccfR3BwMEJDQ/HMM8/A2dlZ6ag26fjx45g7dy6uXr2KiIgIvP7661zFKIjlQtQIv/32G3bv3m1YnVy/fh2enp4YPHgwQkJCEBwcjLZt2yod025otVqkpKRgy5Yt6Nq1K5YsWYKAgAClY9kllguREXQ6HY4cOYLMzExkZWXhp59+ghACPXr0QHBwMEJCQvD000/DyclJ6ah27cSJE5g7dy4KCgowefJkjB07lqsYM2O5EN3HtWvXsHv3bmRkZODbb79FSUkJvL29MWTIEISGhmLIkCFo3bq10jHpT6qqqrBu3Tq8//77eOyxx7BkyRIEBgYqHctusFyI/qS2thaHDx82HNl1/PhxAMCTTz5peBNj79694ejoqHBSaohTp05h7ty5uHTpEiZNmoRx48bxZ2cGLBci/P6ZGnWrkz179qCsrAw+Pj4YOnSoYXVibac8p/+vuroa69evx7vvvotHHnkES5YsQefOnZWOZdNYLmSXampqcPDgQcPq5OTJk5AkCU899ZRhddKrVy++Tm9jTp8+jblz5yI/Px9hYWEYP3489481EZYL2Y3Lly8byiQ7Oxvl5eV44IEH6q1OfHx8lI5JTaympgYbNmzAxo0bERAQgKVLl+Kxxx5TOpbNYbmQzaqqqsKPP/5oOMXK6dOnoVKp8MwzzxiO7OrRowfPS2WncnJyMHfuXOTm5mL8+PGYOHEi34MkI5YL2ZSLFy8aViffffcdKisr0bp1a0OZDB48GN7e3krHJAtRU1ODTZs2Yf369fD398eSJUvQtWtXpWPZBJYLWTWtVosDBw4YVidnzpyBg4MDgoKCDG9ifOKJJ2zmw7OoaZw7dw5z587F2bNnMXbsWISHh3MV00gsF7I6eXl5yMzMREZGBr7//ntoNBq0bdvWcALIQYMGwdPTU+mYZGVqa2vx7rvvIjU1FR07dsSSJUvQvXt3pWNZLZYLWTy1Wo39+/cjIyMDmZmZyM3NhZOTE4KCghAaGoqQkBB07dqVqxOSxfnz5zF37lzk5OTgzTffxOTJk3m2ahOwXMjiCCFw7tw5ZGVlISMjA/v374dWq0WHDh0Mq5OBAwfCw8ND6ahko3Q6Hd5//32kpKSgXbt2WLx4Mf72t78pHcuqsFzIIlRWVmLv3r2GnfEXLlyAs7Mznn32WcPq5NFHH+XqhMwqLy8PsbGxOHXqFP7xj39g6tSpaNasmdKxrALLhRQhhEBOTo6hTA4cOIDq6mr4+fkZVicDBgyAm5ub0lHJzul0OmzduhXJyclo3bo1Fi9ejJ49eyody+KxXMhsysvL8d133xkK5ddff0WzZs3Qv39/w7viAwMDuTohi3ThwgXExsbixIkTGDNmDKZNmwZXV1elY1kslgs1GSEE/v3vfxvK5Mcff0RNTQ0CAwMNZfLcc8+hefPmSkclahCdTocPP/wQSUlJ8PX1xaJFi9C7d2+lY1kklgvJqqysDNnZ2Yb3nVy5cgWurq4YOHCg4aN9+eFNZO0uXbqE2NhYHDt2DK+99hoiIyP5R9KfsFyoUYQQOHHihGF1cvDgQeh0Ojz66KOGfSf9+vXjTlCyOXq9Hv/85z+xZs0atGrVCgsXLkSfPn2UjmUxWC7UKIWFhWjfvj3c3NwwaNAgw+rk4YcfVjoakVlcvnwZ8+bNw7Fjx5CRkcGPtf4Dy4XuyJinRd11TdkRz533ZKmM3QaqqqpMWqHb6jbAj2OjO1q4cCEef/zxO16m0Wjg5OTU6E/zKy4uxsSJExt1H0RNJTU1tcEfKCaEgFarhUqlMurd/Ddu3MArr7xiakSLxnKhO8rJyUFsbOxfvp+WloaNGzfC09MTmzdvRseOHU3+N0aNGsVyIYtV94Fi93PmzBm8++67yMvLg6OjI/r27YuxY8eiRYsW971tVFSUzZYLP8iC7kiSJDg4ONT7SktLw7x587B8+XI899xzCAoKuuP1GvpFZMnu99xWqVTIyMjA2LFj0bZtW8TFxWH69OnIy8vDqFGjcOXKFbveBrhyoQYpKCjAtGnT8PPPP6Nbt24ICQnB1q1bsXr1asyaNUvpeERmd/jwYcTGxmLDhg146qmnDPtO+vbti7S0NIwaNQq7du2Cl5eXskEVwpUL3ZcQAs899xxiYmLQrVs3AL//Vbdnzx7ExMQYteOTyBao1WpMmjQJa9asQZ8+fertlHdwcEB4eDhCQkIwevRou90+WC50X7t370ZRURHeeeedet8PDAyEo6Mjjhw5okwwIgUIITB+/Hg8//zzGDBgwB2vI0kSYmNjodFokJaWZt6AFoLlQvckhMBLL72ETz/99C+fNS9JElatWoWXXnpJoXRE5pefn4+TJ09i+fLl9zyMWKVSYdu2bVi3bh20Wq0ZE1oGlgvd0wcffABnZ2cMGzbsjpeHhYWhsLDQbpf+ZF+EEHjzzTcRHR0NJyen+16/bdu2eOaZZzBjxgwzpLMsLBe6K71ej3HjxiEzM/Ouf6E5ODjAw8MD33zzjZnTEZlfYWEhbt68idGjRzf4NklJSfj+++9RU1PThMksD8uF7mrx4sVo27YtnnzyyXteLyUlBePGjTNTKiLlTJgwAePGjTPqXfXNmzdHly5dsHz58iZMZnlYLnRX8fHx2Lt37303pNdeew3Xr1836ZQxRNaipqYGFy9exJQpU4y+7fr16/HJJ5/Y1fOe5UJ3tX///ga9A1+lUsHZ2RnHjx9v0P3W1NTY5WvQZN3Wr18PPz8/k0575OPjA0dHR5w+fboJklkmlgvdlTEf5fr22283+HXoTZs24bPPPjM1FpHZCSGwadMmrF271qTbS5KEyMhITJs2TeZklovlQrKIiYnBuXPnGrTsnzNnjt0e+0/WqbKyEjqdrlEfJTFmzBhcu3bNbl4aY7mQLFxcXCBJEq5evXrP6wkhUF5ejtDQUDMlI2q8BQsW1DvFiykcHBzg6upqN286ZrmQbF5++WW88cYb97zOTz/9BGdn57+8IZPIkmVkZCA+Pr7R9xMVFYXZs2fLkMjycQsn2aSmpiI7O/uey/5XX30VcXFxZkxF1DjV1dUQQqBVq1aNvq+XX34ZxcXFdvHSGMuFZOPp6QlJklBcXHzHy4UQuHDhAo8UI6uyadMmdOzYUZZPjHR0dIQkSbhx44YMySwby4VkI0kSXn31VYwaNeqOl3/++efw9PRs0GkziCxFenq6rG+ADAoKwqJFi2S7P0vFz3MhWaWlpaFFixYQQtT7S08IgbFjx2L79u0KpiMyjhAC1dXV6N69u2z3GRcXh+DgYNnuz1Jx5UKycnNzQ8uWLfHBBx/U+/6JEydQVVWFIUOGKJSMyHgXL16Eg4ODLC+J1WndujX0er3N73dhuZDsduzYgQkTJkCn0wH4/QSYQ4cORWpqqqwbKVFTi4uLwwsvvCDrfdZ9fPKFCxdkvV9Lw3Ih2fXp0weBgYEYP348iouLERYWBh8fH7z11ltKRyMyyrFjxzBz5kzZ73fo0KFYunSp7PdrSVguJDtJkrBv3z6cOnUKzz33HE6ePIkffviBqxayOk8//TS8vb1lv98ZM2bY/HnGuEOf7sjZ2Rk7d+5s1H1ER0fj119/RceOHXH48OG/XN6Qk2ISKcXJyQmjR4/G/v37m+T+J0+ejMLCwia5b0sgCVvfq0Qm0Wg0Db7un48MaygHBwc4OzsbfTsiczD2o4m1Wi2aNWtm1G0cHBxs9tB8lgs1St1RL5Ik8ZQuZJeEEPjtt99w69YtdOzY0WbLwlj8bUAm27x5M5ydnTF58mSloxApQq/XY/78+Rg0aBB++eUXFsttWC5kkvfffx/jxo3DhAkTkJqaylUL2Z26Yvnyyy+xbNky/Od//qfSkSwKfyOQ0d59912MGzcOEydOxLp161gsZHd0Oh3mzZuHr776CsuXL8d//Md/KB3J4vC3AhklPT0dEyZMQHh4OFJSUnh4MdmdumL5+uuvsWLFCgwfPlzpSBaJ5UINtnHjRoSFhWHKlClITk5msZDd0el0iI2NxTfffIP4+HgMGzZM6UgWi+9zoQbZsGEDwsPDERERgTVr1rBYyO7odDrExMQYPjgsJCRE6UgWjSsXuq/169cjPDwcU6dOZbGQXdLpdJgzZw4yMjKwcuVKFksDsFzonlJTUzFlyhRMnz4dCQkJLBayOzqdDrNnz0ZmZiZWr15tF6fLlwPLhe4qJSUFERERiIqKwqpVq1gsZHd0Oh2io6ORlZWFhIQEfmSEEVgudEfJycmYNm0aZsyYgfj4eBYL2Z3a2lrMmjULu3fvRkJCAgYPHqx0JKvCcqG/SEpKQmRkJGbNmoUVK1awWMju1BVLdnY2EhMTWSwmYLlQPYmJiYiKikJ0dDSWLVvGYiG7U1tbi5kzZ+K7775DYmIiBg0apHQkq8RyIYOEhATMmDEDs2fPxpIlS1gsZHdqamowY8YM7N27F0lJSRg4cKDSkawWy4UAAKtWrcKsWbMQExODxYsXs1jI7tQVy759+5CcnIwBAwYoHcmqsVwIK1euRHR0NGJjY7Fw4UIWC9mdmpoaREVFYf/+/UhOTkb//v2VjmT1+A59O7dixQrExMRg3rx5iIuLY7GQ3amurkZkZCQOHjyItWvX4tlnn1U6kk1gudixZcuWITY2FnFxcZg/f77ScYjMrrq6GtOnT8ehQ4ewdu1a9OvXT+lINoPlYqeWLl2KefPm4Z133sG8efOUjkNkdrcXS0pKCoKCgpSOZFO4z8UOLV68GPPmzcOCBQtYLGSXqqqqMG3aNBw+fBjr1q1jsTQBrlzszMKFC7FgwQIsWrQIMTExSschMruqqipMnToV//d//4d169bhmWeeUTqSTWK52JEFCxZg4cKFWLJkCWbPnq10HCKzq6qqQkREBI4ePYrU1FQ8/fTTSkeyWSwXOyCEMKxWli5diujoaKUjEZmdVqtFREQEjh07htTUVPTp00fpSDaN5WLjhBCIi4vDkiVLsHz5csyaNUvpSERmd3uxpKWloXfv3kpHsnksFxsmhMD8+fOxdOlSxMfHY8aMGUpHIjI7rVaLKVOm4Pjx4ywWM2K52CghBGJjY7F8+XKsXLkSUVFRSkciMjutVovw8HCcPHkSGzZswJNPPql0JLvBcrFBQgjExMQgPj4eq1evxvTp05WORGR2Go0G4eHhOHXqFDZs2IBevXopHcmusFxsjBACc+bMwcqVK5GQkIBp06YpHYnI7DQaDSZNmoTTp09j48aN6Nmzp9KR7A7LxYYIIRAdHY3Vq1cjMTERERERSkciMju1Wo1Jkybhl19+wcaNG9GjRw+lI9kllouNEEJg1qxZWLNmDZKTkzF58mSlIxGZnVqtRlhYGM6cOYP09HT87W9/UzqS3WK52AAhBGbOnInExESsXbsW4eHhSkciMrvKykqEhYXh7Nmz2LhxI4tFYSwXKyCEwI0bN1BRUQF3d3f4+PgYTo0vhEBUVBSSk5ORkpKCSZMmKZyWqGncazuorKzExIkTcf78eaSnp+OJJ55QOC3xxJUWrLS0FElJSQgMDISvry/8/Pzg6+uLwMBAJCUloaSkBJGRkUhOTkZqaiqLhWzS/baDgoICTJgwAbm5udi0aROLxUJIQgihdAj6q6ysLIwcORJqtRrA73+11ZEkCUIIODo6Qq/XIy0tDePHj1cqKlGTach24ODggMDAQHz22Wfo1q2bUlHpT7hysUBZWVkYPnw4NBoNhBD4c//X/X9tbS2EEOjQoYMSMYmaVEO3A51Oh3PnzuHKlStKxKS74MrFwpSWlqJdu3bQaDTQ6/X3vb5KpYKrqysKCgrg5eXV9AGJzIDbgfXjysXCbNmyBWq1ukEbFADo9Xqo1Wps3bq1iZMRmQ+3A+vHlYsFEUIgMDAQ+fn5f3kJ4F4kSYK/vz/Onz9vOHqGyFpxO7ANLBcLcv36dfj6+jbq9j4+PjImIjI/bge2gS+LWZCKiopG3b68vFymJETK4XZgG1guFsTd3b1Rt/fw8JApCZFyuB3YBpaLBfHx8UFAQIDRrxdLkoSAgAC0bNmyiZIRmQ+3A9vAcrEgkiSZfCbjqVOncicm2QRuB7aBO/QtDI/vJ+J2YAu4crEwXl5e2L59OyRJgkp17x+PSqWCJEn44osvuEGRTeF2YP1YLhYoODgYO3fuhKurKyRJ+ssyv+57rq6u2LVrF4YOHapQUqKmw+3AurFcLFRwcDAKCgqQmJgIf3//epf5+/sjMTERV65c4QZFNo3bgfXiPhcrIITAzZs3UV5eDg8PD7Rs2ZI7LcnucDuwLiwXIiKSHV8WIyIi2bFciIhIdiwXIiKSHcuFiIhkx3IhIiLZsVyIiEh2LBciIpIdy4WIiGTHciEiItmxXIiISHYsFyIikh3LhYiIZMdyISIi2bFciIhIdv8PGLOlkfPD3+0AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 500x400 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6383a22f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cbd0f521",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "34fe7629",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(metric='act')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e788b91",
   "metadata": {},
   "source": [
    "Remove insignificant neurons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ed4800ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = model.prune()\n",
    "model.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61c8eeb1",
   "metadata": {},
   "source": [
    "Resize the figure using the \"scale\" parameter. By default: 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5cb8d57e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(scale=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "67305f39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 200x160 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(scale=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "51c722ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x1600 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(scale=2.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03d4bf1b",
   "metadata": {},
   "source": [
    "If you want to see sample distribution in addition to the line, set \"sample=True\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c6d24148",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(sample=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3fa482a",
   "metadata": {},
   "source": [
    "The samples are more visible if we use a smaller number of samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3856bcb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.get_act(dataset['train_input'][:20])\n",
    "model.plot(sample=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fa7ca2c",
   "metadata": {},
   "source": [
    "If a function is set to be symbolic, it becomes red"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3d502880",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r2 is 0.9991374611854553\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor(0.9991)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fix_symbolic(0,1,0,'x^2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f8f93b9c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e75a0760",
   "metadata": {},
   "source": [
    "If a function is set to be both symbolic and numeric (its output is the addition of symbolic and spline), then it shows up in purple"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "17df5fed",
   "metadata": {},
   "outputs": [],
   "source": [
    "model.set_mode(0,1,0,mode='ns')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b5b13363",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fb710b46",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
